For the technology of the next-generation communication, MIMO transmitting has been intensively developed. The technique of MIMO improves a transmission capacity through the use of a number of transmitting antennas and a number of receiving antennas. In MIMO communication, signals transmitted from a number of transmitting antennas are received in a state of being jammed, by respective receiving antennas in a receiver.
FIG. 5 illustrates MIMO communication system having a number M of transmitting antennas and a number N of receiving antennas. The transmitter end (Tx) transmits transmitting signals x1, x2, . . . , and xM through M transmitting antennas and the receiver end (Rx) receives received signals yl, y2, . . . , and yN.
Here, the received signals yi (i=1 through N) received by the receiving antennas #i can be represented by the following formula (1) where a channel value between the transmitting antenna #j (j=1 through M) and the receiving antenna #i is represented by hij.
                              r          i                =                              ∑                          j              =              1                        M                    ⁢                                    h              ij                        ⁢                          d              j                                                          (        1        )            
Accordingly, the received signals by the receiving antennas #1 through #N are represented by the following formula (2).
                              [                                                                      y                  1                                                                                                      y                  2                                                                                    ⋮                                                                                      y                  N                                                              ]                =                              [                                                                                h                    11                                                                                        h                    12                                                                    …                                                                      h                                          1                      ⁢                      M                                                                                                                                        h                    21                                                                                        h                    22                                                                    …                                                                      h                                          2                      ⁢                      M                                                                                                                    ⋮                                                  ⋮                                                  ⋱                                                  ⋮                                                                                                  h                                          N                      ⁢                                                                                          ⁢                      1                                                                                                            h                                          N                      ⁢                                                                                          ⁢                      2                                                                                        …                                                                      h                    NM                                                                        ]                    ⁡                      [                                                                                x                    1                                                                                                                    x                    2                                                                                                ⋮                                                                                                  x                    M                                                                        ]                                              (        2        )            
The formula (2) becomes the following formula (3) when the received signal vector, the transmitted signal vector, and the matrix are represented by the symbols y, x, and H, respectively.y=Hx  (3)
Here, the transmitted signal vector x, the received signal vector y, and the matrix (channel matrix) H are represented by the following formulae (4), (5), and (6), respectively. The symbol T in the formulae (4) and (5) represents transposition.
                    x        =                              [                                                                                x                    1                                                                                        x                    2                                                                    …                                                                      x                    M                                                                        ]                    T                                    (        4        )                                y        =                              [                                                                                y                    1                                                                                        y                    2                                                                    …                                                                      y                    N                                                                        ]                    T                                    (        5        )                                H        =                  [                                                                      h                  11                                                                              h                  12                                                            …                                                              h                                      1                    ⁢                    M                                                                                                                        h                  21                                                                              h                  22                                                            …                                                              h                                      2                    ⁢                    M                                                                                                      ⋮                                            ⋮                                            ⋱                                            ⋮                                                                                      h                                      N                    ⁢                                                                                  ⁢                    1                                                                                                h                                      N                    ⁢                                                                                  ⁢                    2                                                                              …                                                              h                  NM                                                              ]                                    (        6        )            
At the receiver end, the transmitted signals, which have been transmitted in the form of being jammed through the channel and then received, need to be separated from one another (hereinafter called MIMO decoding). The transmitted signal vector x is estimated from the received signal vector y and the channel matrix H of the formula (3).
There have been proposed various methods for MIMO decoding, such as MLD (Maximum Likelihood Detection), MMSE (Minimum Mean Square Error), and V-BLAST(Vertical—Bell Laboratories Layered Space Time).
In the meantime, methods have been proposed in which transmitted signals are easily estimated through the use of QR decomposition in MIMO decoding (see, for example, Patent Reference 1, and Non-Patent References 1 and 2 below).
Specifically, since the channel matrix H is decomposed into a unitary matrix (orthogonal matrix) Q and an upper triangular matrix R through QR decomposition, as denoted in the following formula (7), multiplication of the above formula (3) on the right by the unitary matrix QH obtains the following formula (8). An upper triangular matrix is one whose bottom-left elements below the diagonal are zero.
                    H        =        QR                            (        7        )                                                                    z              =                            ⁢                                                Q                  H                                ⁢                y                                                                                        =                            ⁢                                                                    Q                    H                                    ⁡                                      (                    QR                    )                                                  ⁢                x                                                                                        =                            ⁢              Rx                                                          (        8        )            
Thereby, the received signals z are identical to products of the transmitted signals x and the upper triangular matrix R, which makes it easier to estimate the transmitted signals.
There have already been proposed some methods of MIMO decoding using QR decomposition; for example, Non-Patent Reference 1 realizes the estimation of transmitted signal by yielding only a small amount of calculation because of a combination with MLD.
Further, Non-Patent Reference 2 proposes a method of adopting a LST (Layered Space Time) architecture and thereby enhancing the reception capability.
In a 3×3 MIMO system having the number of transmitting antennas and the number of receiving antennas both being three, for example, a method using QR decomposition converts the formula (2) into the following formula (9), and obtains the following formula (10) through the use of QR decomposition.
                              [                                                                      y                  1                                                                                                      y                  2                                                                                                      y                  3                                                              ]                =                              [                                                                                h                    11                                                                                        h                    12                                                                                        h                    13                                                                                                                    h                    21                                                                                        h                    22                                                                                        h                    23                                                                                                                    h                    31                                                                                        h                                          3                      ⁢                                                                                          ⁢                      2                                                                                                            h                    33                                                                        ]                    ⁡                      [                                                                                x                    1                                                                                                                    x                    2                                                                                                                    x                    3                                                                        ]                                              (        9        )                                          [                                                                      z                  1                                                                                                      z                  2                                                                                                      z                  3                                                              ]                =                              [                                                                                r                    11                                                                                        r                    12                                                                                        r                    13                                                                                                0                                                                      r                    22                                                                                        r                    23                                                                                                0                                                  0                                                                      r                    33                                                                        ]                    ⁡                      [                                                                                x                    1                                                                                                                    x                    2                                                                                                                    x                    3                                                                        ]                                              (        10        )            
The QR decomposition is carried out in conformity with the Gram-Schmidt orthgonalization with the result that a unitary matrix Q and an upper triangular matrix R are obtained from the channel matrix H.
In a 3×3 MIMO system, the Gram-Schmidt orthgonalization results in the upper triangular matrix R and the unitary matrix Q being represented by the following formulae (11) and (12), respectively.
                    R        =                              [                                                                                r                    11                                                                                        r                    12                                                                                        r                    13                                                                                                0                                                                      r                    22                                                                                        r                    23                                                                                                0                                                  0                                                                      r                    33                                                                        ]                    =                      [                                                                                                                          u                      1                                                                                                                                                      q                      1                      H                                        ⁢                                          h                      2                                                                                                                                  q                      1                      H                                        ⁢                                          h                      3                                                                                                                    0                                                                                                                u                      2                                                                                                                                                      q                      2                      H                                        ⁢                                          h                      3                                                                                                                    0                                                  0                                                                                                                u                      3                                                                                                                ]                                              (        11        )                                                      Q            =                          [                                                                                          q                      1                                                                                                  q                      2                                                                                                  q                      3                                                                                  ]                                ,                                    q              i                        =                                          [                                                                                                    q                                                  1                          ⁢                          i                                                                                                                                    q                                                  2                          ⁢                          i                                                                                                                                    q                                                  3                          ⁢                          i                                                                                                                    ]                            T                                      ⁢                                  ⁢                  where          ,                                    (        12        )                                          H          =                      [                                                                                h                    1                                                                                        h                    2                                                                                        h                    3                                                                        ]                          ,                              h            i                    =                                    [                                                                                          h                                              1                        ⁢                        i                                                                                                                        h                                              2                        ⁢                        i                                                                                                                        h                                              3                        ⁢                        i                                                                                                        ]                        T                                              (        13        )                                          u          i                =                              h            i                    -                                    ∑                              j                =                1                                            i                -                1                                      ⁢                                          (                                                      q                    j                    H                                    ⁢                                      h                    i                                                  )                            ⁢                              q                j                                                                        (        14        )                                          q          i                =                              u            i                                                          u              i                                                                      (        15        )            
The symbol H in the element qjH represents a complex conjugate.
The transmitted signals are sequentially estimated specifically by firstly estimating x3 from the above formula (10), then estimating x2 on the basis of the estimated x3, and finally estimating x1 on the basis of both x3 and x2.
Here, it is preferable that the accuracy of the estimation of x3 is increased as high as possible in consideration of the procedure in which x3 is firstly estimated and x2 is estimated on the basis of the estimated x3. For the above, the element r33 in an upper triangular matrix preferably has a larger value as large as possible.
Manipulation of elements in the upper triangular matrix R needs interchanging column vectors of the channel matrix H. For example, interchanging the second column with the third column of the channel matrix H of the formula (9) results in the following formula (16), which is then QR-decomposed into the following formula (17).
                              [                                                                      y                  1                                                                                                      y                  2                                                                                                      y                  3                                                              ]                =                              [                                                                                h                    11                                                                                        h                    13                                                                                        h                    12                                                                                                                    h                    21                                                                                        h                    23                                                                                        h                    22                                                                                                                    h                    31                                                                                        h                    33                                                                                        h                    32                                                                        ]                    ⁡                      [                                                                                x                    1                                                                                                                    x                    3                                                                                                                    x                    2                                                                        ]                                              (        16        )                                          [                                                                      z                  1                  ′                                                                                                      z                  2                  ′                                                                                                      z                  3                  ′                                                              ]                =                              [                                                                                r                    11                    ′                                                                                        r                    12                    ′                                                                                        r                    13                    ′                                                                                                0                                                                      r                    22                    ′                                                                                        r                    23                    ′                                                                                                0                                                  0                                                                      r                    33                    ′                                                                        ]                    ⁡                      [                                                                                x                    1                                                                                                                    x                    3                                                                                                                    x                    2                                                                        ]                                              (        17        )            
Here, differently from the upper triangular matrix of the above formula (10), the upper triangular matrix of the formula (17) preferably selects a larger element r33 from the viewpoint of error propagation in the process of estimation of transmitted signals.
Actually, Non-Patent Reference 2 proposes a method of improving the reception capability by interchanging columns of the channel matrix X such that the element r33 is larger and then QR decomposition.
Patent Reference 1: Japanese Patent Publication No. 2003-273837
Non-Patent Reference 1: Kenichi HIGUCHI et al., “Adaptive Selection Algorithm of Surviving Symbol Replica Candidates in QRM-MLD for MIMO Multiplexing Using OFCDM Wireless Access”, Technical Report of IEICE, RCS2004-69, May, 2004
Non-Patent Reference 2: D. Wubben J, at et al., “Efficient Algorithm for Detecting Layered Space-Time Codes”, 4th International ITG conference on source and channel and coding, Berlin, January 2002
The method of Non-Patent Reference 2 controls the diagonal elements of an upper triangular matrix to be larger (by interchanging columns) in the process of the QR decomposition. Description will now be made with reference to FIG. 6, assuming a 3×3 matrix. Firstly, each column vector of the matrix H in FIG. 6(1) is subjected to the following calculation:|h11|2+|h21|2+|h31|2, |h12|2+|h22|2+|h32|2, |h13|2+|h23|2+|h33|2 
As a consequence, a column corresponding to the minimum value of these three sums is determined.
In this example, the first column is assumed to be the minimum and, as depicted in FIG. 6(2), is subjected to the calculation in order to be converted into [r11,0,0]T.
Next, for the second and the third columns, the sums of the squares of respective column vectors are similarly calculated to find the smaller sum. This example assumes the third column is smaller and, as denoted in FIG. 6(3), the second column is interchanged with the third column to create the upper triangular matrix as denoted in FIG. 6(4).
This method creates an upper triangular matrix, focusing only on the diagonal elements with the intention of lessening an error of X3 by increasing the element r33 in the formula (10) as large as possible.
However, the method focuses only on the diagonal elements as described above, in other words, does not take the remaining elements in consideration. Consequently, the accuracy of the estimation of x3 is insufficient, and in the event of occurrence of an error in x3, the same error propagates to the subsequent judgment on the transmitting signals, so that the required capability of reception (decoding) cannot be obtained.